Pierre Hodara and Ioannis Papageorgiou
We aim to prove Poincaré inequalities for a class of pure jump Markov processes inspired by the model introduced by Galves and Löcherbach to describe the behavior of interacting brain neurons. In particular, we consider neurons with degenerate jumps, i.e., which lose their memory when they spike, while the probability of a spike depends on the actual position and thus the past of the whole neural system. The process studied by Galves and Löcherbach is a point process counting the spike events of the system and is therefore non-Markovian. In this work, we consider a process describing the membrane potential of each neuron that contains the relevant information of the past. This allows us to work in a Markovian framework.
Aline Duarte, Ricardo Fraiman, Antonio Galves, Guilherme Ost and Claudia D. Vargas
It has been repeatedly conjectured that the brain retrieves statistical regularities from stimuli. Here, we present a new statistical approach allowing to address this conjecture. This approach is based on a new class of stochastic processes, namely, sequences of random objects driven by chains with memory of variable length.
The whole paper is available here.
Sandro Gallo and Nancy L. Garcia
Consider the following coverage model on \mathbb {N}, for each site i \in \mathbb {N}associate a pair (\xi _i, R_i) where (\xi _i)_{i \ge 0} is a 1-dimensional undelayed discrete renewal point process and (R_i)_{i \ge 0} is an i.i.d. sequence of \mathbb {N}-valued random variables. At each site where \xi _i=1 start an interval of length R_i. Coverage occurs if every site of \mathbb {N} is covered by some interval. We obtain sharp conditions for both, positive and null probability of coverage. As corollaries, we extend results of the literature of rumor processes and discrete one-dimensional Boolean percolation.
The whole paper is available here.
Marco Antonio Cavalcanti Garcia and Claudia Domingues Vargas
Spasticity is a sensorimotor disorder widely recognized as one of the features that contribute to patients’ disability. Transcutaneous electric neural stimulation (TENS/SES) has been adopted in spasticity rehabilitation as an alternative to pharmacological agents. Although previous studies have reported clinical benefits of TENS/SES in relieving spasticity, there is no clarity on how and whether this therapeutic modality affects specific neural circuitries. Thus, this systematic review aimed to verify the efficacy of TENS/SES in the control of spasticity and its consequences in spinal and corticospinal excitability. This study was carried out according to PRISMA recommendations using SCOPUS, PubMed, BVS, Google Scholar and BASE databases screening, which provided 483 references. Six additional records were found from other sources. All these records were submitted to a filtering process following the eligibility criteria, and 44 studies were selected for further analysis. Ten were replicas. Consequently, 34 studies were read in full with the aim of checking their eligibility criterion, which resulted in 10 manuscripts for qualitative synthesis. Even though they evaluated the effects of TENS/SES both at the spinal and/or corticospinal levels, the electrophysiological results seem to be inconsistent, corroborating the lack of agreement between them and with clinical outcomes.
The whole paper is available here.
Ricardo Felipe Ferreira is a mathematician who, during his doctoral research, was guided by the RIDC NeuroMat associated investigator Alexsandro Giacomo Grimbert Gallo (UFSCar). During the first semester of 2019, Ferreira defended his doctoral thesis, in which NeuroMat research is a highlight.
